1. CP V IOLATION IN B 0 S  J/   CDF (and D0) Joe Boudreau University of Pittsburgh ≠ 1

2. A very brief abstract of this talk first. The following topics will be developed: CDF and D0 use B 0 s  J/  to measure CKM phases. We determine from this decay the quantity  s. This is in exact analogy to B factory measurement of the , an angle of the unitarity triangle. The standard model makes very precise predictions for both angles. But other new particles & processes, lurking potentially in quantum mechanical loops such as box diagrams and penguin diagrams can change the prediction. V ub * V ud V tb * V td V cb * V cd  V ub * V us V tb * V ts V cb * V cs ss 2

3. T HE “ LOCAL ” CONNECTION Studies of CPV in B 0 s  J/  at the Tevatron go back to 2006, since then this has remained a “hot topic”. Significant updates are in the works right now From the U.K. Oxford team are major players (Farrukh Azfar and Louise Oakes); I recommend inviting them in the near future to deliver the punch line. 3

4. “N OTHING IS CREATED, NOTHING IS DESTROYED, EVERYTHING IS TRANSFORMED.” e.g 2H + O  H 2 0 This maxim from the 18 th century is wrong. Here is a recipe to produce hydrogen  Lavoisier 4

5. A THOUGHT EXPERIMENT WITH A BOX OF NOTHING : Take a box of nothing. Heat it up to above the T EM, the temperature of the electroweak phase transition ~ 100 GeV Cool rapidly Open the box and you will find something … ordinary baryonic matter. 5

6. 6

7. CKM P HYSICS & COSMOLOGY WMap measures: The SM has all of the ingredients (Sakharov conditions) to generate the 100% Baryon Asymmetry of the Universe, but the quantity: where J is the Jarlskog Invariant Depends on quark Masses and on CP violation, thus it can be studied “in the laboratory”. 7

8. V ub * V ud + V tb * V td + V cb * V cd =0 The quantity “A” is the area of the“Unitarity Triangle” V ub * V ud V tb * V td V cb * V cd  W+W+ u d W+W+ u s W+W+ u b W+W+ c d W+W+ c s W+W+ c b W+W+ t d W+W+ t s W+W+ t b 8

9. There are six unitarity triangles that can be formed, and all of them have the same area: The area of any one of these triangles quantifies how much CP violation one gets (with three generations of quark). 9

10. There are 12 observed instances of CP violation. 1. Indirect CP violation in the kaon system (  K ) 2. Direct CP violation in the kaon system  ’/  3. CP Violation in the interference of mixing and decay in B 0 → J/  K 0. 4. CP Violation in the interference of mixing and decay in B 0 ->  ’K 0 5. CP Violation in the interference of mixing and decay in B 0 ->K + K - K s 6. CP Violation in the interference of mixing and decay in B 0 ->  +  - 7. CP Violation in the interference of mixing and decay in B 0 ->D *+ D - 8. CP Violation in the interference of mixing and decay in B 0 ->f 0 K 0 s 9. CP Violation in the interference of mixing and decay in B 0 ->  0 10. Direct CP Violation in the decay B 0  K -  + 11. Direct CP Violation in the decay B   12. Direct CP Violation in the decay B      # 3 is important to us because: predictions are precise. there is a similarity w/ the B 0 s  J/  10

11. Very famous measurement of CP Asymmetries in B 0  J/  K 0 s |B 0 > | J/  K 0 s > V ub * V ud V tb * V td V cb * V cd  BABAR, BELLE have used this decay to measure precisely the value of sin(2  ) an angle of the bd unitarity triangle. There was a fourfold ambiguity http://ckmfitter.in2p3.fr/ 11

12. |B 0 > | P 0 > | P  > | P || > |+-K0s0>|+-K0s0> Babar, Belle resolve an ambiguity in  by analyzing the decay B 0  J/  K 0 * which is B  V V and measures sin(2  ) and cos(2  ) This involves complicated angular analysis (to be described) J/  K 0 * |B 0 > Phys.Rev. D71 (2005) 032005 Phys.Rev.Lett. 95 (2005) 091601 12

13. |B s 0 > | P 0 > | P  > | P || > |+-K+K->|+-K+K-> J/  |B s 0 >  J/  is an almost exact analogy, except this system also contains a difference in lifetime/width) |B s 0 > 13

14. b d s c c W W W d B 0 → J/  K 0* b s s c c WW W s B s 0 → J/   The decay B 0 s J/  obtains from the decay B 0 J/ K 0* by the replacement of a d antiquark by an s antiquark We are measuring not the (bd) unitarity triangle but the (bs) unitarity triangle: 14

15. B 0 s →J/   B 0 s →J/   is two particles decaying to three final states.. Two particles: Three final states:J/   in an S waveCP Even J/   in a D wave CP Even J/   in a P wave CP Odd Light, CP-even, shortlived in SM Heavy, CP-odd, longlived in SM A supposedly CP even initial state decays to a supposedly CP odd final state…. like the neutral kaons Measurement needs  ≠0 but not flavor tagging. The polarization of the two vector mesons in the decay evolves with a frequency of  m s Measurement needs flavor tagging, resolution, and knowledge of  m s 15

16. Time dependence of the angular distributions: use a basis of linear polarization states of the two vector mesons { S, P, D}  { P , P ||, P 0 } CP odd states decay to P  CP even states decay to P ||, P 0 If [H,CP] ≠ 0 Then The polarization correlation depends on decay time. Angular distribution of decay products of the J/  and the  analyze the rapidly oscillating correlation.  m s ~ 17.77 ps -1. A.S. Dighe, I. Dunietz, H. J. Lipkin, and J. L. Rosner, Phys. Lett. B 369, 144 (1996), 184 hep-ph/9511363. 16

17. This innocent expression hides a lot of richness: * CP Asymmetries through flavor tagging. * sensitivity to CP without flavor tagging. * sensitivity to both sin(2  s ) and cos(2  s ) simultaneously. * Width difference * Mixing Asymmetries An analysis of an oscillating polarization. The measurement is a flavor-tagged analysis of time-dependent angular distributions 17

18. The flavor-tagged analysis of B 0 s  J/  is a post B 0 s mixing analysis. * phenomenologically related * same flavor tagging technology, too. * CP violation analysis needs  m s from mixing analysis 18

19. There are two states in the B 0 s system, the so-called “Flavor eigenstates” They evolve according to the Schrödinger eqn and M,  Hermitian Matrices M: Dispersive diagrams  : Absorptive diagrams u, c B 0 s –B 0 s Flavor Oscillations 19

20. The magnitude of the box diagram gives the oscillation frequency m. The phase of the diagram determines the complex number q/p, with magnitude of very nearly 1 (in the standard model). Mass eigenstates are superpositions of flavor eigenstates governed by constants p, q: And an initially pure |B 0 s > evolves (oscillates) mixing probability: 20

21. In general the most important components of a general purpose detector system, for B physics, is: tracking. muon [+electron] id triggering. 21

22. CDF Detector showing as seen by the B physics group. Muon chambers for triggering on the J/ →  +  - and  Identification. Strip chambers, calorimeter for electron ID Central outer tracker dE/dX and TOF system for particle ID r < 132 cm B = 1.4 T for momentum resolution. 22

23. L00: 1.6 cm from the beam. 50  m strip pitch Low mass, low M-S. For B 0 s mixing: SVXII can trigger on hadronic decays!! Excellent vertex resolution from three silicon subsystems: SVX IIISL 23

24. The D0 Silicon tracker….. surrounded by a fibre tracker at a distance 19.5 cm < r <51.5 cm now augmented by a high-precision inner layer (“Layer 0”) 71 (81)  m strip pitch factor two improvement in impact parameter resolution 24

25. Mixing is an important constraint on the Unitarity Triangle: Mixing probability Mixing occurs when a B 0 s decays as a B 0 s. Decay to a flavor specific eigenstate tags the flavor at decay: B 0 s  D s  ; B 0 s  D s  ; B 0 s  D s l One of three tagging algorithms tags the flavor at production. Good triggering, full reconstruction of hadronic decays, excellent vertex resolution, and high dilution tagging are all essential for this measurement, which made news in 2006. 25

26. Δm s = 17.77 ± 0.10(sta) ± 0.07(sys) ps -1 |V td /V ts | = 0.2060 ± 0.0007 (exp) + 0.0081 – 0.0060 (theor) (PRL 97, 242003 2006) Δ m s = 18.56 ± 0.87(stat) ps -1 (D0 CONF Note 5474) 26

27. Two techniques for initial state “flavor tagging” b, b quarks are always produced in pairs; b quark always opposite b b antiquark always opposite b  Flavor-specific decay modes (eg semileptonic decays) of the opposite side b, or jet charge can be used to determine the sign of the b quark on the opposite side. The fragmentation chain produces weak correlations between b quark flavor and the sign of nearby pions and kaons in the fragmentation chain  Procedure to select leading  ±, K ± can be optimized to obtain the highest quality tag. 27

28. Each tagger returns: A decision (B or B) An estimate of the quality of that decision (dilution D)  = tag efficiency D = 1-2w w = mistag rate D 2 = effective tagging efficiency Performance of the flavor tag in CDF 28

29. The quality of the Prediction of dilution Can be checked against the data: We reconstruct a sample Of B ± decays in which one knows the sign of the B meson. We then “predict” the sign of the meson and plot the predicted dilution vs the actual dilution. Separately for B + and B - Scale (from lepton SVT this sample; take the difference B + /B - as an uncertainty). 29

30. Flavor Tagging Performance and Validation SST +OST:  D 2 = 4.68 ± 0.54% Each tag decision comes with an error estimate validated: 1. Using B ± (OST) 2. In the B 0 s mixing (SST) SST:  D 2  3.6% OST:  D 2  1.2% 30

31. This innocent expression hides a lot of richness: * CP Asymmetries through flavor tagging. * sensitivity to CP without flavor tagging. * sensitivity to both sin(2  s ) and cos(2  s ) simultaneously. * Width difference * Mixing Asymmetries An analysis of an oscillating polarization. The measurement is a flavor-tagged analysis of time-dependent angular distributions 31

32. The analysis of B 0 s →J/  can extract these physics parameters: The exact symmetry.. … is an experimental headache. The measurement of  s and  are correlated; from theory one has the relation  = 2|  12 |cos(2  s ) with |  12 | = 0.048 ± 0.018 and A. Lenz and U. Nierste, J. High Energy Phys. 0706, 072 (2007). 32

33. CDF, 2506 ± 51 events.. And in D0, 1967 ± 65 total.. … but 2019 ± 73 tagged events, all tagged. …[and 3150 in 2.8 fb -1 ] Next, we’ll run through the CDF analysis, show what you get from flavor tagging, then show the D0 results. 33

34. Results from 1.7 fb -1 of untagged decays. 34

35. Phys.Rev.Lett.98:121801,2007 35

36. Results untagged analysis Standard Model Fit (no CP violation) HQET: c  (B 0 s )= (1.00±0.01) c  (B 0 ) PDG: c  (B 0 ) = 459 ±0.027 m Phys.Rev.Lett.100:121803,2008 36

37. More results, untagged analysis Applying the HQET lifetime constraint: 37

38. An angular analysis can also be applied to the decay B 0 -> J/K * to extract amplitudes ~ CP even / Odd fractions in the final state: 38

39. Angular fit projections B 0  J/  K 0* Angular fit projections B 0  J/  39

40. A consistent picture of the CP Odd/Even fraction in B 0 →J/  K*, B 0 s →J/  in CDF, Babar, and Belle experiments: B0sB0s B0B0 B0B0 B0B0 R. Itoh et al. Phys Rev. Lett. 98, 121801, 2007 (Belle) B. Aubert et al. PRD 76 (2007) 031102 (Babar) 40

41. This plot is Feldman-Cousins confidence region in the space of the parameters 2  s and  The likelihood for the untagged analysis has a higher degree of symmetry (    +   with  s  -  s ) than the tagged analysis. As you will soon see  41

42. Results from 1.35 fb -1 of tagged decays. 42

43. Tagged analysis: likelihood contour in the space of the parameters  s and  One ambiguity is gone, now this one remains 43

44. Constrain strong phases  || and   to BaBar Values (for B 0  J/  K* !!) Constrain  s to PDG Value for B 0 Apply both constraints. B. Aubert et al. (BABAR Collaboration), Phys. Rev. D 71, 032005 (2005). using values reported in: 44

45. The standard model predictions of  s and  data consistent with the CDF data at the 15% confidence level, corresponding to 1.5 Gaussian standard deviations. One dimensional Feldman-Cousins confidence intervals on 2  s (  treated as a nuisance parameter): 2  s  [0.32, 2.82] at the 68% CL. Assuming |  12 | = 0.048 ± 0.018 and the assumption of mixing-induced CP violation: 2  s  [0.24,1.36] U [1.78, 2.90] at the 68% CL. If we additionally constrain the strong phases  || and   to the results from B 0  J/  K *0 decays and the B s mean width to the world average B d width, we find 2  s  [0.40, 1.20] at 68% CL 45

46. A Feldman-Cousins confidence region in the  s -  plane is the main result. This interval is based on p-values obtained from Toy Monte Carlo and represents regions that contain the true value of the parameters 68% (95%) of the time. The standard model agrees with the data at the 15% CL arXiv:0712.2397v1 46

47. D0 Strategy (quite different from CDF). Strong phases vary around the world average values ( for B 0  J/  K* !!) Uncertainty taken to be ±  /5 Is this justified? Theory now estimates the difference between the strong phases in the two decays to be < 10 o. J. Rosner and M. Gronau, Phys.Lett.B669:321-326,2008 ) Obtain “point estimates” in these all of these fits. Note, D0 has a different name for the CP violation parameter:  s J/  = -2  s CP = CP fit,  s J/  floating SM = Standard model fit,  s J/  floating NP = New Physics fit,  s J/  and  constrained by the assumption of mixing- induced CP violation. 47

48. Comparison of |Amplitude| 2 (CDF and D0) 48

49. D0 Result: arXiv:0802.2255v1 49

50. Likelihood contours for just  and for just  s =-2  s 50

51. Outlook Note  s = -2  s Fluctuation or something more, it does go in the same direction. CDF estimates confidence level at 15% using p-values to obtain Ln(L/L 0 ) D0 estimates confidence level a 6.6% using the probability to extract a lower value than seen in the data, from toy. 51

52. UTFit group has made an “external” combination. “re-introduces” the ambiguity into the D0 result. does so by symmetrizing; cannot fully undo the strong phase constraint. arXiv:hep-ph/0803.0659 52

53. Combined by HFAG: D0 then performed a fit w/o strong phase constraints 53

54. Summer ‘08 Interim result: CDF adds the second half of its data, but without calibration of PID and TOF, after first 1.35 fb -1 only OST tagging is used, and no PID used in selection.  D 2 = 1.8% for 2 nd half of data SM p-value is 7%. Fluctuation did not go away D0 produces a confidence region without the strong phase constraints. 54

55. ff fluctuation? discrepancy? p-value = 0.034 2.12  from SM p-value 0.02 2.33  from SM 55

56. 56 4 th Generation? Outline of arXiv:0803.1234v3 George W.S. Hou WMap measures: The SM has all of the ingredients (Sakharov conditions) to generate the 100% Baryon Asymmetry of the Universe, but the quantity: falls short by ten orders of magnitude. A possible solution is a 4 th generation where J is the Jarlskog Invariant Assuming m t’ > m b’ > m t and taking, m t’ = 300 GeV, the author predicts large negative values of  s : -0.7 < sin(2  s ) < -0.5 CDF Direct Search Limit: m t’ > 256 GeV/c 2 ; m b’ > 268 GeV/c 2 can provide an enhancement of 10 13 or more

57. What’s expected next? Analysis of full 5.2 fb -1 dataset. dE/dx calibrated and performing in selection + tagging. D0 analyzing 6.0 fb -1 Same side kaon tagging being applied to the full sample (not just 1.35 fb -1 as in ‘08 interim update. 57

58. S-WAVE CONTAMINATION ? 58

59. When B 0 s  J/  K + K - ; m(K + K - )~ 1020 MeV/c 2 and L(K + K - ) = 1 we call that B 0 s  J/  When L=0 we call that the S-wave; it is CP-even and nonresonant. Additional terms in the probability density are easy to handle; instead of just this: You also need this for the S-wave component: Don’t forget the mass dependence. Or P-wave S-wave interference. Or the proper detector re-normalization after the detector sculpting. 59

60. Those terms have been included in the likelihood function so we plan to (finally) respond to the question about S-wave contamination by not neglecting it, this time. Plots show tests of the new fitter. 60

61. C ONCLUSIONS B 0 s  J/   is an important and precise test of the origin of CP violation in the standard model. D0 has performed a flavor-tagged analysis of 2.8 fb -1. CDF has used 1.35 fb -1 of data in a first analysis then added another 1.45 fb -1 of data (but with OST only). There were hints of new physics, at the 2.33  level. Updates to 5 fb -1 are in progress at CDF, to 6 fb -1 at D0 Look forward to the definitive statement from the Tevatron before too long. And then we all look forward to very high statistics analyses from the LHCB 61

62. 62

63. V ub * V ud = O( 3 ) V tb * V td = O( 3 ) V cb * V cd = O( 3 )  V ub * V us = O( 4 ) V tb * V ts = O( 2 ) V cb * V cs = O( 2 ) ’’ With = 0.2272± 0.0010 A = 0.818 (+0.007 -0.017)  = 0.221 (+0.064-0.028)  = 0.340 (+0.017-0.045) One easily obtains a prediction for  s : 2  s = 0.037±0.002 63

64. The  A “anomaly” may also have to do with b  s Direct CP in B +  K +  0 and B 0  K +  - are generated by the b  s transition. These should have the same magnitude. But Belle measures (4.4  ) Including BaBar measurements: > 5  The electroweak penguin can break the isospin symmetry But then extra sources of CP violating phase would be required in the penguin Lin, S.-W. et al. (The Belle collaboration) Nature 452,332–335 (2008). 64

65. Example of new physics: a fourth generation quark that contributes to the Electroweak Penguin Would have other measureable consequences: e.g. an impact on mixing induced CP violation in B 0 s mesons. Wei-Shu Hou, arXiv:hep-ph/0803.1234 65

66. 66

67. where i = 0, para, perp and B B An analysis of the decay can be done with either a mix of B and B mesons (untagged) or with a partially separated sample (flavor tagged). Latter is more difficult and more powerful. These expressions are: * used directly to generate simulated events. * expanded, smeared, and used in a Likelihood function. * summed over B and ̅ B (untagged analysis only) reference material 67

68. Proper decay time: distance between production & decay….. Beam profile ~ 30 microns. L xy c  = L xy /sin = L xy M B /P T … transformed into the rest frame of the B meson: Resolution is about 76 fs for the J/  decay mode 68

69. Semileptonic asymmetry We have assumed so far that: and thus | | = 1.. To a very good approximation. In higher order however |q| ≠ |p| and | |≠1 (at the level of 1-| | < 2.5 x 10 -3 ) A s SL = 0.020 ± 0.028 (CDF) http://www- cdf.fnal.gov/physics/new/bottom/070 816.blessed-acp-bsemil / A s SL = 0.0001 ± 0.0090 (stat) (D0, dimuon) A s SL = 0.0024 ± 0.0117(stat) +0.0015 -0.0024 (syst) (D0, semileptonic B 0 s decays) Phys. Rev. D 76, 057101 (2007) HQET   /M s 12 =(49.7 ±9.4) ±10 −4 Semileptonic asymmetry: For mixing-induced CP violation D0 Conf Note 5730

70. 70 combined CDF/D0 CDF/D0 + A s sl + assumption of mixing induced CP violation. Under these assumptions A s sl constrains  and  s. Green is 69% CL allowed region. … with the following effect on the contours: